Attitude and position estimation from vector observations
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This paper introduces three novel methods to evaluate attitude and position from vector observations using a vision-based technology camera. The first approach, called Linear Algebra Resection Approach (LARA), solves for attitude and position simultaneously and can be used in the lost-in-space case, when no approximate solution is available. The solution is shown to be the left eigenvector associated with the minimum singular value of a rectangular data matrix. The second and third approaches, called Attitude Free Approaches (AFA), recast the problem into a nonlinear system of equations in terms of the unknown position only. Two different methods are proposed to solve this nonlinear set of equations. The First AFA (FAFA) uses a least-square Newton-Raphson iterative procedure and is particularly suitable for the recursive case, while the Second AFA (SAFA) uses the toric resultant to eliminate two variables from the attitude-free system of nonlinear polynomial equations and a discretization of the Cauchy integral theorem to quickly isolate the solution. SAFA can be used either in the lost-in-space or in the recursive cases. Final numerical tests quantify the robustness of these methods in the case of measurements affected by noise.